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Factor. $\newline$ $4m^2 + 64m - 68$

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Factor quadratics

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Q. Factor.

\newline

4m^2 + 64m - 68

Identify Numbers: First, let's look for two numbers that multiply to $4 \times -68$ (which is $-272$ ) and add up to $64$ .
Find Correct Numbers: The numbers that work are $68$ and $-4$ because $68 \times -4 = -272$ and $68 - 4 = 64$ .
Rewrite Middle Term: Now, we rewrite the middle term using the numbers we found: $4m^2 + 68m - 4m - 68$ .
Factor by Grouping: Next, we factor by grouping. Group the first two terms and the last two terms: $(4m^2 + 68m) - (4m + 68)$ .
Factor Common Factor: Factor out the common factor in each group: $4m(m + 17) - 4(m + 17)$ .
Factor Out Common Factor: Now, we can see that $(m + 17)$ is a common factor. So, we factor it out: $(m + 17)(4m - 4)$ .
Factor Out $4$ : Finally, we can factor out a $4$ from the second binomial to make it look neater: $(m + 17)(4)(m - 1)$ .
Final Factored Form: So, the factored form of $4m^2 + 64m - 68$ is $(m + 17)(4m - 4)$ , but we can also write it as $4(m + 17)(m - 1)$ to show the common factor of $4$ .

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